Finite Group Databasebeta

← #16858311

Subgroups — #16858311

Order 3968.

360 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14521745C211yesmaximal, characteristic, complemented
2#14521448C211yesmaximal, characteristic, complemented
3#14521373C211yesmaximal, characteristic, complemented
4#14521370C211yesmaximal, characteristic, complemented
5#14521362C211yesmaximal, characteristic, complemented
6#14521360C211yesmaximal, characteristic, complemented
7#14521349C211yesmaximal, characteristic, complemented
8#14521346C211yesmaximal, characteristic, complemented
9#14521300C211yesmaximal, characteristic, complemented
10#14521300C211yesmaximal, characteristic, complemented
11C4×#92479C211yesmaximal, characteristic, complemented
12#14521127C211yesmaximal, characteristic, complemented
13#14521092C211yesmaximal, characteristic, complemented
14#14521089C211yesmaximal, characteristic, complemented
15C31×#553C211yesmaximal, characteristic, complemented
16C31×#126—21no—
17C31×#125C2211yescharacteristic
18C31×#123—21no—
19C31×#121—21no—
20C31×#121C2211yescharacteristic
21C31×#121C2211yescharacteristic
22C4×D4×C31—21no—
23C4×D4×C31C2211yescharacteristic
24C4×D4×C31C2211yescharacteristic
25C31×#117C2211yescharacteristic
26C2×C4⋊C4×C31C2211yescharacteristic
27#11758516—21no—
28C2×#92479C2211yescharacteristic
29#11758507C2211yescharacteristic
30#11758507C2211yescharacteristic
31#11758503C2211yescharacteristic
32C2×C4⋊Dic31C2211yescharacteristic
33C2×#92474C2211yescharacteristic
34C2×#92474C2211yescharacteristic
35#11758475—21no—
36#11758460—21no—
37(C22⋊D31)⋊C4—21no—
38C4×D124C2211yescharacteristic
39#11758447C2211yescharacteristic
40#11758420C2211yescharacteristic
41#11758420C2211yescharacteristic
42#11758420C2211yescharacteristic
43C22⋊(C31⋊C8)C2211yescharacteristic
44C22⋊(C31⋊C8)C2211yescharacteristic
45#11758397C2211yescharacteristic
46#11758397C2211yescharacteristic
47#11758397C2211yescharacteristic
48#11758396C2211yescharacteristic
49#11758396C2211yescharacteristic
50#11758396C2211yescharacteristic
51#11758396C2211yescharacteristic
52#11758395C2211yescharacteristic
53#11758395C2211yescharacteristic
54#11758395C2211yescharacteristic
55#11758395C2211yescharacteristic
56#11758395C2211yescharacteristic
57C4⋊(C31⋊C8)C2211yescharacteristic
58C4×C31⋊C8C2211yescharacteristic
59C2×D4×C31—21no—
60C2×D4×C31—21no—
61C2×D4×C31D411yescharacteristic
62C2×D4×C31C2311yescharacteristic
63C22×C4×C31—21no—
64C22×C4×C31—21no—
65C22×C4×C31C2311yescharacteristic
66C22×C4×C31C2311yescharacteristic
67C2×C22⋊D31—21no—
68C2×C22⋊D31—21no—
69C22×Dic31—21no—
70C2×D124C2311yescharacteristic
71C2×C4×D31—21no—
72C4⋊C4×C31—21no—
73C4⋊C4×C31—21no—
74C4⋊C4×C31—21no—
75C4⋊C4×C31D411yescharacteristic
76C4⋊C4×C31C2311yescharacteristic
77C4⋊C4×C31C2311yescharacteristic
78C4⋊C4×C31C2311yescharacteristic
79C22⋊C4×C31—21no—
80C22⋊C4×C31—21no—
81C22⋊C4×C31—21no—
82C22⋊C4×C31—21no—
83C22⋊C4×C31D411yescharacteristic
84C22⋊C4×C31D411yescharacteristic
85C42×C31—21no—
86C42×C31C2311yescharacteristic
87C22⋊Dic31—21no—
88#92479—22no—
89(C2×D31)⋊C4—21no—
90(C2×D31)⋊C4—21no—
91(C2×D31)⋊C4—21no—
92C4⋊Dic31—21no—
93C4⋊Dic31C2311yescharacteristic
94C4⋊Dic31C2311yescharacteristic
95C4⋊Dic31C2311yescharacteristic
96Dic31⋊C4—21no—
97Dic31⋊C4—21no—
98C4×Dic31—21no—
99#92474—22no—
100#92474—22no—
101C2×C31⋊C8C2311yescharacteristic
102C2×C31⋊C8C2311yescharacteristic
103C2×C31⋊C8C2311yescharacteristic
104C2×C31⋊C8C2311yescharacteristic
105C23×C31—21no—
106C23×C31C2×D411yescharacteristic
107C23×C31C2×D411yescharacteristic
108C22×D31—21no—
109D4×C31—21no—
110D4×C31—21no—
111D4×C31—41no—
112D4×C31—42no—
113D4×C31—81no—
114C2×C4×C31—21no—
115C2×C4×C31—21no—
116C2×C4×C31—21no—
117C2×C4×C31—21no—
118C2×C4×C31—21no—
119C2×C4×C31—21no—
120C2×C4×C31—21no—
121C2×C4×C31—81no—
122C2×C4×C31—81no—
123C2×C4×C31C2×D411yescharacteristic
124C2×C4×C31C2×D411yescharacteristic
125C2×C4×C31C2×D411yescharacteristic
126C2×C4×C31C2×D411yescharacteristic
127C2×C4×C31C2411yescharacteristic
128C22⋊D31—42no—
129C22⋊D31—81no—
130C2×Dic31—21no—
131C2×Dic31—21no—
132C2×Dic31—21no—
133C2×Dic31—81no—
134D124—21no—
135D124—21no—
136C4×D31—81no—
137C31⋊C8—21no—
138C31⋊C8—21no—
139C31⋊C8—21no—
140C31⋊C8#4112yes—
141#3355—311nomaximal, Sylow
142C22×C31—21no—
143C22×C31—21no—
144C22×C31—21no—
145C22×C31—21no—
146C22×C31—21no—
147C22×C31—21no—
148C22×C31—41no—
149C22×C31—41no—
150C22×C31—41no—
151C22×C31C22×D411yescharacteristic
152C2×D31—41no—
153C2×D31—41no—
154C2×D31—41no—
155C4×C31—21no—
156C4×C31—21no—
157C4×C31—21no—
158C4×C31—21no—
159C4×C31—41no—
160C4×C31—41no—
161C4×C31—41no—
162C4×C31C2×#4111yescharacteristic
163C4×C312−1+411yescharacteristic
164Dic31—41no—
165Dic31—41no—
166Dic31—41no—
167#553—311no—
168#553D3111yescharacteristic, complemented
169#499—311no—
170#482—311no—
171#482—311no—
172#480—311no—
173#480—311no—
174#478—311no—
175#478—311no—
176#469—311no—
177#469—311no—
178C4×D8—311no—
179#436—311no—
180#428—311no—
181#428—311no—
182C2×C31—41no—
183C2×C31—41no—
184C2×C31—81no—
185C2×C31#54711yescharacteristic
186C2×C31#57511yescharacteristic
187C2×C31#57611yescharacteristic
188D31—81no—
189C2×D8—311no—
190C2×M16—311no—
191C2×M16—311no—
192#126—21no—
193#126—621no—
194#125—311no—
195#125C2×D3111yescharacteristic
196#123—21no—
197#123—621no—
198#121—21no—
199#121—311no—
200#121—311no—
201#121—621no—
202#121C2×D3111yescharacteristic
203#121C2×D3111yescharacteristic
204C4×D4—21no—
205C4×D4—311no—
206C4×D4—621no—
207C4×D4C2×D3111yescharacteristic
208C4×D4C2×D3111yescharacteristic
209#117—311no—
210#117C2×D3111yescharacteristic
211C2×C4⋊C4—311no—
212C2×C4⋊C4C2×D3111yescharacteristic
213#107—311no—
214#107—311no—
215#107—311no—
216#107—311no—
217#107—311no—
218#106—311no—
219#106—311no—
220#106—311no—
221#106—311no—
222C4⋊C8—311no—
223#102—311no—
224#102—311no—
225#102—311no—
226#102—311no—
227#102—311no—
228#102—311no—
229C22⋊C8—311no—
230C22⋊C8—311no—
231C4×C8—311no—
232C31#335511yescharacteristic, complemented, Sylow
233C2×D4—21no—
234C2×D4—21no—
235C2×D4—311no—
236C2×D4—621no—
237C2×D4—621no—
238C2×D4C22⋊D3111yescharacteristic
239C2×D4C22×D3111yescharacteristic
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—621no—
243C22×C4—621no—
244C22×C4C22×D3111yescharacteristic
245C22×C4C22×D3111yescharacteristic
246D8—622no—
247M16—622no—
248M16—622no—
249C2×C8—311no—
250C2×C8—311no—
251C2×C8—311no—
252C2×C8—311no—
253C4⋊C4—21no—
254C4⋊C4—21no—
255C4⋊C4—21no—
256C4⋊C4—311no—
257C4⋊C4—311no—
258C4⋊C4—311no—
259C4⋊C4—621no—
260C4⋊C4—621no—
261C4⋊C4—621no—
262C4⋊C4C22⋊D3111yescharacteristic
263C4⋊C4C22×D3111yescharacteristic
264C4⋊C4C22×D3111yescharacteristic
265C4⋊C4C22×D3111yescharacteristic
266C22⋊C4—21no—
267C22⋊C4—21no—
268C22⋊C4—21no—
269C22⋊C4—21no—
270C22⋊C4—621no—
271C22⋊C4—621no—
272C22⋊C4—621no—
273C22⋊C4—621no—
274C22⋊C4C22⋊D3111yescharacteristic
275C22⋊C4C22⋊D3111yescharacteristic
276C42—21no—
277C42—621no—
278C42C22×D3111yescharacteristic
279C23—21no—
280C23—621no—
281C23C2×C22⋊D3111yescharacteristic
282C23C2×C22⋊D3111yescharacteristic
283D4—21no—
284D4—21no—
285D4—41no—
286D4—42no—
287D4—81no—
288D4—621no—
289D4—621no—
290D4—1242no—
291D4—2481no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—81no—
300C2×C4—81no—
301C2×C4—621no—
302C2×C4—621no—
303C2×C4—621no—
304C2×C4—2481no—
305C2×C4—2481no—
306C2×C4C2×C22⋊D3111yescharacteristic
307C2×C4C2×C22⋊D3111yescharacteristic
308C2×C4C2×C22⋊D3111yescharacteristic
309C2×C4C2×C22⋊D3111yescharacteristic
310C2×C4C23×D3111yescharacteristic
311C8—312no—
312C8—621no—
313C8—621no—
314C8—621no—
315C22—21no—
316C22—21no—
317C22—21no—
318C22—21no—
319C22—21no—
320C22—21no—
321C22—41no—
322C22—41no—
323C22—41no—
324C22—1241no—
325C22—1241no—
326C22—1241no—
327C22C22×C22⋊D3111yescharacteristic
328C4—21no—
329C4—21no—
330C4—21no—
331C4—21no—
332C4—41no—
333C4—41no—
334C4—41no—
335C4—1241no—
336C4—1241no—
337C4—1241no—
338C4#41×D3111yescharacteristic
339C4#1175856711yescharacteristic
340C2—41no—
341C2—41no—
342C2—81no—
343C2—2481no—
344C2#1452169811yescharacteristic
345C2#1452184711yescharacteristic
346C2#1452185211yescharacteristic
subgroupG/H
centerC22C22×C22⋊D31
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC31×#553C2
socleC22×C31C22×D4
hypercenter#553D31
hypocenterC31#3355
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C4×D4 ◁ #553

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #14521745C2semidirect
2. #14521448C2semidirect
3. #14521373C2semidirect
4. #14521370C2semidirect
5. #14521362C2semidirect
6. #14521360C2semidirect
7. #14521349C2semidirect
8. #14521346C2semidirect
9. #14521300C2semidirect
10. #14521300C2semidirect
11. C4×#92479C2semidirect
12. #14521127C2semidirect
13. #14521092C2semidirect
14. #14521089C2semidirect
15. C31×#553C2semidirect
168. #553D31semidirect
232. C31#3355semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#145217452
#145214482
#145213732
#145213702
#145213622
#145213602
#145213492
#145213462
#145213002
C4×#924792
#145211272
#145210922
#145210892
C31×#5532
#335531